Igusa CM Invariants Database

An Igusa CM invariant is specified by a sequence of three polynomials [ H₁(x), G₂(x)/N₂, G₃(x)/N₃], such that H₁(x), G₂(x), and G₃(x) are in Z[x],

H₁(i₁) = 0,

i₂ = G₂(i₁)/N₁N₂,

i₃ = G₃(i₁)/N₁N₃,

where N₁ = H₁'(i₁), and N₂ and N₃ are integers, and

i₁ = I₄I₆/I₁₀,

i₂ = I₂³I₄/I₁₀,

i₃ = I₂²I₆/I₁₀,

in terms of the Igusa-Clebsch invariants [ I₂, I₄, I₆, I₁₀ ].

Degree: [Non-normal] [Cyclic]

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Degree 13 Igusa CM invariants of cyclic (C4) fields: 5

Number	Igusa invariants	Conductor	Components	Quartic invariants	Class number	Class group
1)	[317, 317, 15533]	[1]	1	[317, 317, 15533]	13	C₁₃
2)	[269, 269, 6725]	[1]	1	[269, 269, 6725]	13	C₁₃
3)	[509, 509, 61589]	[1]	1	[509, 509, 61589]	13	C₁₃
4)	[397, 397, 3573]	[1]	1	[397, 397, 3573]	13	C₁₃
5)	[557, 557, 27293]	[1]	1	[557, 557, 27293]	13	C₁₃